Partial derivatives

Suppose u = x^4*y + y^2*z^3, where x = r*s*e^t, y = r*s^2*e^-t, and z = sin(t)r^2*s. Find du/ds.
So I believe you plug in x, y, and z into the equation to get:
u = (rse^t)^4*(rs^2e^-t) + (rs^2e^-t)^2*(sin(t)r^2s)^3
And I know you have to treat all the variables except s as a constant, but I'm just getting confused with all the numbers. Thanks!